Differentiate `sin^(-1)x`with respect to `cos^(-1)sqrt(1-x^2)`,if `-1ltaxlt1`

Explanation

Let` theta=sin ^{-1} x`

`implies sin theta={x}`

` implies cos theta=sqrt{1-{x}^{2}}`

On differentiating `sin theta` w.r.t. `x`,

`cos theta frac{d theta}{d x}=1`

`implies frac{d theta}{d x}=frac{1}{cos theta}`

`implies frac{{d} theta}{{dx}}=frac{1}{sqrt{1-{x}^{2}}}`

Let `gamma=cos ^{-1} sqrt{1-x^{2}}`

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